📚 Topic Summary
The Product of Powers rule is a fundamental concept in algebra. It states that when multiplying two exponents with the same base, you can simplify the expression by adding the exponents. This simplifies calculations and is essential for working with polynomials and other algebraic expressions.
For example, consider $x^m * x^n$. According to the product of powers rule, this simplifies to $x^{m+n}$. This rule applies to any real number base, whether it is a variable or a constant.
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Base |
A. The number of times the base is multiplied by itself |
| 2. Exponent |
B. A symbol or letter representing an unknown quantity |
| 3. Variable |
C. The number that is raised to a power |
| 4. Product of Powers |
D. $a^m * a^n = a^{m+n}$ |
| 5. Coefficient |
E. A numerical or constant quantity placed before and multiplying the variable in an algebraic expression |
✍️ Part B: Fill in the Blanks
The Product of Powers rule states that when multiplying exponents with the same _____, you _____ the exponents. For example, $2^3 * 2^2 = 2^{3+2} = 2^5 = _____. Therefore, the Product of Powers rule provides a simple way to _____ expressions with exponents.
🤔 Part C: Critical Thinking
Explain, in your own words, why the Product of Powers rule works. Use examples to illustrate your explanation.